A controversial part of the Jewish ritual, known as metzitzah b'peh, involves the practitioner, or mohel, placing his mouth around the baby's penis to suck the blood to clean the wound.

Health department officials said one of the two infected babies developed a fever and lesion on its scrotum about a week after the circumcision and tests for HSV-1 came back positive.

The New York City Board of Health voted in 2012 to require parents sign a written consent that warns them of the risks of the metzitzah b'peh.

However, the parents for neither of the infected boys had signed the form, said Jay Varma, deputy commissioner for disease control at the Department of Health and Mental Hygiene.

Varma said it was "too early to tell" if the infections will affect the long-term health of the babies.

Neonatal herpes infections can cause death or disability among infants, according to data from the Centers for Disease Control and Prevention.

Since 2000, there have been 13 cases of herpes linked with the particular circumcision ritual, including two deaths and two other cases of babies who suffered related brain damage.

"There is no safe way an individual can perform oral suction on an open wound," Dr. William Schaffner, chair of preventive medicine at Vanderbilt University was quoted saying by ABCNews. "These terrible infections are completely preventable. They should not occur in the 21st century with our scientific knowledge."

Some rabbis told ABCNews last year that they opposed the parental waiver requirement on religious grounds. They also said in the previous interview the particular circumcision ceremony is performed tens of thousands of times a year throughout the world and that safeguarding the life of a child is one of the religion's highest priorities.